(Q10) The base of a triangle is 4 cm longer than its altitude. If the area of the triangle is 48 sq.cm, then find its base and altitude.

Answer

Let the altitude of the triangle h = x cm

Then its base 'b' = x + 4.

Area=
1
2
 × base × height
=
1
2
(x + 4)(x)
=
x2+4x
2
By problem
x2+4x
2
 = 48
x2 + 4x = 2 × 48
x2 + 4x - 96 = 0
x2 + 12x - x - 96 = 0
x(x + 12) - (x + 12) = 0
(x + 12)(x - ) = 0
x + 12 = 0 (or) x - = 0
x = -12 (or) x =
But x can't be negative.
∴ x= and x + 4 = +4=

Hence altitude = cm and base = cm.